In a known two-row rolling bearing arrangement mounted on a shaft supported in a housing and having adjustable prestress in the axial direction, the first rolling bearing is located in the housing or on the shaft and the outer ring of the second rolling bearing can be displaced in the housing by using a spring on one side which forces the first rolling bearing away and an adjustable member for supplying the spring force on the other side (U.S. Pat. No. 1,399,959, wherein the adjustable member is a ring screwed onto the housing. In spite of the involved arrangement of the two threads, the limits of adjustment are relatively wide as compared to the degree of fineness of prestress adjustment obtainable by the ring setting and reached by respective loading or relieving of the spring, even if a thread of particularly low pitch is used, which further increases the degree of involvement. Therefore the known arrangement is used only to compensate for a discernible axial play caused by wear after a long service life of the bearing by resetting the respective rings, thereby resulting in a new adjustment of the prestress. The actual original and newly adjusted magnitudes of the prestress are only approximmately known and the magnitude can be adjusted only to approximate a predetermined magnitude. The motion of the adjustable member within the course of a thread has also the general disadvantage that a one-sided load is applied upon the outer ring, as a result of which the loosely fitted outer ring gets misaligned, which has a detrimental effect upon bearing operation. The known arrangement is therefore not suited for use in bearing arrangements which require high-precision operation.